ESPN's Joe Schad confirmed Thursday the deal had been completed.
Wilson, 42, becomes the fifth African-American coach hired this offseason among 26 openings in FBS. Earlier Thursday, NCAA president Mark Emmert expressed concern that minorities are not being given a fair shot in college athletics.
Wilson spent the last six seasons at LSU, where he coached multiple players who reached the NFL. In last weekend's NFL wild-card games alone, the leading rushers for the Houston Texans (Alfred Blue), Kansas City Chiefs (Spencer Ware) and Cincinnati Bengals (Jeremy Hill) were all former Wilson protégés at LSU.
Wilson was also the driving force behind LSU signing running back Leonard Fournette, a fellow New Orleans native who was the nation's No. 1 overall prospect in 2014.
Multiple entities, including NFL.com and Rivals.com, have named Wilson as their recruiter of the year in recent seasons, and he had another star-studded class lined up at LSU before accepting the UTSA job. With less than three weeks left until national signing day, ESPN.com rates LSU's 2016 recruiting class first in its team rankings.
Before arriving at LSU, Wilson made coaching stops at Tennessee in 2009, Southern Miss in 2008 and Ole Miss from 2005 to '07.
Coker, 67, stepped down on Jan. 5 after launching the UTSA program in 2009 and coaching the Roadrunners for five seasons.
UTSA went 8-4 in 2012, its first season as an FBS transitional program, and went 7-5 in 2013 after joining Conference USA. However, the Roadrunners slipped to 4-8 in 2014 and 3-9 in 2015, and Coker resigned after the season.